arXiv 0812.10322008-12-04math.DGmath.MG

多面体Hilbert几何的Lipschitz特征

Lipschitz Characterisation of Polytopal Hilbert Geometries

Constantin Vernicos

备注：: Extends our previous result with B. Colbois and P. Verovic arXiv:0804.1620v1. Main Theorem independently and differently proved by Andreas Bernig
发表信息：: Osaka J. Math. 52:215-235 (2014)

摘要：

证明了凸集的Hilbert几何与赋范向量空间的双Lipschitz等价当且仅当凸集是多面体。

We prove that the Hilbert Geometry of a convex set is bi-lipschitz equivalent to a normed vector space if and only if the convex is a polytope.

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